Convert the following binary numbers to decimal. 1. 1100 2. 10100 3. 10011 4. 10101 5. 11100
The correct answer and explanation is:
Let’s convert the binary numbers to decimal:
- 1100
To convert from binary to decimal, each digit represents a power of 2, starting from the rightmost digit (the least significant bit). So:
11002=1×23+1×22+0×21+0×201100_2 = 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 0 \times 2^0 =1×8+1×4+0×2+0×1=8+4+0+0=12= 1 \times 8 + 1 \times 4 + 0 \times 2 + 0 \times 1 = 8 + 4 + 0 + 0 = 12
So, 1100 in binary equals 12 in decimal.
- 10100
Now for 10100:
101002=1×24+0×23+1×22+0×21+0×2010100_2 = 1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 0 \times 2^0 =1×16+0×8+1×4+0×2+0×1=16+0+4+0+0=20= 1 \times 16 + 0 \times 8 + 1 \times 4 + 0 \times 2 + 0 \times 1 = 16 + 0 + 4 + 0 + 0 = 20
So, 10100 in binary equals 20 in decimal.
- 10011
For 10011:
100112=1×24+0×23+0×22+1×21+1×2010011_2 = 1 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 =1×16+0×8+0×4+1×2+1×1=16+0+0+2+1=19= 1 \times 16 + 0 \times 8 + 0 \times 4 + 1 \times 2 + 1 \times 1 = 16 + 0 + 0 + 2 + 1 = 19
So, 10011 in binary equals 19 in decimal.
- 10101
For 10101:
101012=1×24+0×23+1×22+0×21+1×2010101_2 = 1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 =1×16+0×8+1×4+0×2+1×1=16+0+4+0+1=21= 1 \times 16 + 0 \times 8 + 1 \times 4 + 0 \times 2 + 1 \times 1 = 16 + 0 + 4 + 0 + 1 = 21
So, 10101 in binary equals 21 in decimal.
- 11100
For 11100:
111002=1×24+1×23+1×22+0×21+0×2011100_2 = 1 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 0 \times 2^0 =1×16+1×8+1×4+0×2+0×1=16+8+4+0+0=28= 1 \times 16 + 1 \times 8 + 1 \times 4 + 0 \times 2 + 0 \times 1 = 16 + 8 + 4 + 0 + 0 = 28
So, 11100 in binary equals 28 in decimal.
Summary of results:
- 1100 in binary = 12 in decimal
- 10100 in binary = 20 in decimal
- 10011 in binary = 19 in decimal
- 10101 in binary = 21 in decimal
- 11100 in binary = 28 in decimal
The process of converting from binary to decimal involves understanding that each binary digit (bit) represents a power of 2. By multiplying each bit by the corresponding power of 2 and summing the results, the binary number can be converted to decimal.